On Baire class one functions on a product space

摘要

We show that every Baire class one function on a countable product of metric spaces is the pointwise limit of a sequence of continuous functions, each depending only on finitely many coordinates of the argument. It is proved also that this result does not extend to higher Baire classes (with continuous functions replaced by arbitrary ones). (C) 2015 Elsevier B.V. All rights reserved.